Now I would like to know if with such a visa one has also to leave via these border points.

Indeed, is this procedure also valid if a EU citizen enters Kaliningrad via Poland, and leaves it in less than 72 hours via Lithuania? Or will she have to apply for a "traditional" visa in that case, as the border crossings with Lithuania are not part of this special visa program.

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On the same site nothing is indicated whether the entry and exit points must be the same. The only thing that is prescribed on the official site are the points of entry, which given the fact that Khrabrovo Airport is on the list of possible entry points means that the origination country doesn't have to be Poland.

There is a tourist site konigsberg.ru where this exact question was asked before, so your exit to Lithuania is not an issue.